AGITATION Performance of Propellers in Liquid-Solid Systems' ARTHUR W. HIXSON AND SIDNEY J. BAU-M Columbia University, New York, N. Y.
Previously derived relations are applied to a study of the rate of dissolution of solids in liquids in a series of geometrically similar vessels fitted with propeller stirrers. It is found that the dissolution constant, IC, for any particular liquid-solid system under isothermal conditions is a function of the product of speed and size factor, nd, and this relation holds for several different agitator designs. The results for four liquidsolid combinations in propeller agitators over a temperature range of 6-45' C. are correlated by the equation :
the speed remained fairly constant over the entire range; but with the larger sizes comparatively large fluctuations (20-30 r. p. m.) from any set speed took place, particularly when the motor was runnin at or near its rated load. This was probably due to the nonuniform nature of the load and the small size of the driving motor. Where large fluctuations occurred, an average speed was estimated. The propellers were rotated in a direction to force the liquid down toward the bottom of the vessel. The propellers and shafts of the three larger sizes were given a heavy coat of a methacrylate varnish. The 26.0-cm. vessel and impeller were coated with the same varnish after the runs with benzene were completed. The materials, experimental procedure, and analytical methods were the same as those employed with the turbine agitators (2).
Experimental Results From the results of the experimental runs, dissolution constant K was calculated by the approximate integrated form of the cube root law previously derived (2): K== A A 9
wo - w
The methods and results indicate the utility of model experiments in prediction of agitator performance.
where and
I
Am =
A0
-
A
2.303 log 2A%'
N AN EARLIER paper (2) a method was presented for the correlation of data on liquid-solid mass transfer in a series of geometrically similar agitation vessels. This method was suggested as a tool for predicting agitator performance on the basis of model experiments, and its validity was corroborated for one particular agitator design. The work is extended in the present paper to show that this method is also applicable in cases where the agitator design is varied and where mass transfer data are obtained over a range of temperatures.
(3)
The values for K are shown in Table I. The results of runs made by Hixson and Wilkens (4) with the system benzoic acid-water at 25' C. in baffled turbine agitators are shown in Table 11. The latter dissolution constants were recalculated to conform to the equations and dimensions used in the present investigation. Although particles of four different sizes and shapes were used in the present and previous experiments, there was no indication that size or shape had any influence on the value of the dissolution constant. As will be shown later, a single correlation for all systems in any one agitator design is possible, independent of the size or shape of the solid particles. It may be that the range of sizes used in this study was so small that the effect of this variable, if any, was not indicated in the experimental results. As closely as could be determined by examination and measurement, the particles maintained their shape throughout the dissolution process. Measurement of the residual benzoic acid particles after 60 per cent of their initial weight was dissolved indicated that these had the same relative dimensions as the original particles. The work of Hixson and Crowell (3) showed that the dissolution constant for solids dissolving in liquids remained substantially constant until approximately 70 per cent or more of the original solid was dissolved. This is some indication of the validity of the assumption that the relation between weight and surface is constant throughout the major portion of the dissolution process. In the present investigation values for K are based on the dissolution of 50 per cent or less of the initial weight of solid.
Apparatus Four three-blade marine type propellers, having nominal diameters of 7.61, 10.2, 12.7, and 17.8 cm., were used. Each propeller was built according to the so-called square pitch design where the pitch is equal to the diameter. The propellers were approximately geometrically similar, although the largest had a smaller hub length in relation to its diameter than did any of the others. The propellers were used in the 26.0-, 35.9-, 45.7-, and 61.0-om. vessels previously described (3). The size ratios are indicated approximately in Figure 1. The ratios of tank diameter to nominal propeller diameter are 3.41, 3.52, 3.60, and 3.42, respectively. An average value of 3.5 is shown in Figure 1. The framework, used with the turbine agitators and described in detail in the earlier paper ( d ) , was modified so that the propeller shafts entered the cylindrical agitation vessels at an angle of 60" to the horizontal, as shown in Figure 1. The gear ratio on the framework was changed t o 2: 1, and sometimes 1:1, to obtain higher rotational speeds of the impeller. In this manner a range of speeds of 200-1600 r. p. m. was possible. The same tachometer device was employed to read the shaft speed as was used with the turbine type impellers. For the smaller propellers The first two paper8 of this series appeared in April (page 478) and November (page 1433), 1941.
120
INDUSTRIAL AND ENGINEERING CHEMISTRY
January, 1942
SIMILAR TABLE I. Mass TRANSFER DATAIN GEOMEITRICALLY
26.0
BzOH-water
35.9
46.7
61.0
26.0
BnOH-benzene
26.0
Rook salt-water
35.9
45.7
61.0 BEOH-ethyleneglyool
26.0
12.5 12.5 13.8 8.95 11.0 13.4 15.3 18.0 5.00 8.33 6.67 10.0 13.3 15.0 8.03 10.6 9.17 11.8 13.0
26.0 25.0 26.0 25.6 25.7 26.7 25.8 25.8 24.8 26.0 25.0 25.0 25.0 23.4 25.1 25.0 24 3 24.2 24.2
1.00
7.68 9.01 10.3 10.3 10.1 2.71 3.87 5.07 6.37 7.63 6.37 5.07 7.63 9.02 11.5 13.6 7.73 12.7 15.3 18.0 20.7 23.0 25.8 7.63 9.01 11.5 12.9 11.5 11.6 11.5 11.5 11.5 11.5 11.5 5.06 7.63 11.5 10.3 12.7 15.3 18.0 6.37 6.36 7.63 9.01 11.5 12.9 16.3 18.0
25.2 25.2 25.1 25.0 25.0 21.7 21.8 21.9 22.0 25.0 25.0 25.0 24.7 24.8 24.8 24.8 23.5 23.5 25.0 25.0 25.0 25.0 25.0 25.5 25.5 25.5 25.5 6.4 12.9 18.4 30.0 34.9 39.0 45.4 24.6 24.6 24.6 25.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 23.0 23.0 23.0 23.0
1.00
5.06 7.63 10.3 7.63 9.02 11.5 13.6 15.3 18.0 20.7
25.7 25.7 25.7 26.8 27.0 27.0 27.2 27.5 27.9 28.0
1.00
1.00
0.878
1.00
1.00
1.00
1.00 1.11
1.17 X 10-6 1.15 1.15 1.17 1.17 1.17 1.17 1.17 1.14 1.17 1.15 1.15 1.15 1.11 1.15 1.15 1.13 1.13 1.13
0.00455 0.00483 0.00483 0.00252 0.00383 0.00434 0.00511 0.00794 0.00195 0.00320 0.00276 0.00379 0.00672 0.00790 0.00332 0.00434 0.00362 0.00489 0.00597
325 325 359 233 286 348 398 468 180 299 240 359 477 539 288 381 329 424 466
9.66 9.45 1.05 6.86 8.45 1.03 1.18 1.39 7.20 1.23 9.64 1.44 1.92 2.08 1.16 1.53 1.30 1.68 1.84
0.00890 0.00890 0.00892 0.00894 0.00894 0.00968 0.00965 0.00962 0.00960 0.00894 0.00894 0.00894 0.00605 0.00605 0.00605 0.00605 0.00925 0.00925 0.00894 0.00894 0.00894 0.00894 0.00894 0.00885 0.00885 0.00885 0.00885 0.0146 0.0121 0.0105 0.00800 0.00725 0.00670 0.00595 0.00902 0.00902 0.00902 0.00894 0.00894 0.00894 0.00894 0.00894 0.00894 0.00894 0.00894 0.00936 0.00936 0.00936 0.00936
1.15 1.15 1.15 1.15 1.15 1.06 1.06 1.07 1.07 1.15 1.15 1.16 1.44 1.44 1.44 1.44 1.54 1.54 1.61 1.61 1.61 1.61 1.61 1.63 1.63 1.63 1.63 9.2 X 10-6 1.12 x 101.32 1.84 2.08 2.29 2.68 1.59 1.59 1.59 1.61 1.61 1.61 1.61 1.61 1.61 1.61 1.61 1.52 1.52 1.52 1.52
0.00236 0.00412 0.00473 0.00567 0.00572 0.00149 0.00232 0.00346 0.00383 0.00713 0.00595 0.00457 0.00307 0.00357 0.00409 0.00552 0.00346 0.00487 0.00656 0.00713 0.00758 0.00826 0.00870 0.00340 0.00390 0.00430 0.00475 0.00252 0.00313 0.00355 0.00471 0.00503 0.00590 0,00692 0.00268 0.00361 0.00541 0.00470 0.00642 0.00680 0.00752 0.00327 0.00366 0.00431 0.00453 0.00610 0.00720 0.00790 0.00885
232 349 412 471 462 166 236 310 388 466 389 310 198 235 299 354 201 331 397 469 636 599 669 198 234 299 335 835 335 335 335 335 336 335 182 274 414 371 457 548 647 229 291 349 412 525 590 698 825
1.19 1.79 2.12 2.41 2.37 1.05 1.49 1.96 2.46 3.19 2.66 2.12 7.48 8.85 1.13 1.33 5.65 9.30 1.16 1.36 1.56 1.74 1.95 5.81 6.87 8.79 9.85 5.31 6.41 7.39 9.70 1.07 1.16 1.30 7.24 1.09 1.65 1.49 1.84 2.20 2.60 9.21 1.49 1.78 2.11 2.56 2.88 3.41 4.03
0.00881 0.00881 0.00881 0.150 0.150 0.150 0.148 0.146 0.143 0.142
1.65 1.65 1.65 3.2 X 10-' 3.2 3.2 3.1 3.1 3.0 3.0
0.00374 0.00695 0.00820 9.83 X lo-* 1.22 x 10-4 1.87 2.07 2.25 2.54 3.12
309 466 630
2.14 3.22 4.36 3.81 X IO4 4.51 5.75 6.90 7.86 9.44 1.08 X 106
indicated that the In the first Paper (2)dimensional results for liquid-solid mass transfer in a series of geometrically similar agitation vessels of any one design could be oorrelated by an equation of the type: Kd
AGITATORS
0.00875 0.00894 0.00894 0.00883 0.00880 0.00880 0.00879 0.00879 0 * 00898 0.00875 0.00894 0.00894 0.00894 0.00927 0.00892 0.00894 0.00908 0.00909 0.00909
Correlation and Discussion of Data
d
PROPELLER
121
(*)
X 106 X 108 X 10' X 106 X X X X
106 106 106 106
X 108 X 106 X 106
X 106
X 10'
X 108 X 10' x 106
x
108 X 101
10,100 10,900 10,900 5,600 8,500 9,660 11,400 17,600 6.140 9,820 8,610 11,800 21,000 25,600 10.400 13,600 11,200 15,500 19,000
748 776 776 752 752 752 761 751 786 748
369 392 392 204 310 352 416 642 219 359 310 424 754 886 372 489 395 547 670
776
776 776 836 776 776 803 804 804
9,400 16,400 18.800 22,500 22,800 8,560 13,400 21,300 21,800 37,800 31,600 24,200 5,550 6,450 7,380 9,960 5,830 8,220 10,600 11,500 12,200 13,300 14.000 5;420 6,220 6,860 7,580 7,120 7 260 7:OOO 6,660 6,290 6,700 6,720 6,050 8,150 12,200 10.500 14.300 15,200 16 800 7:300 10,100 12.200 12,900 18,400 21,600 23,800 26,600
774 774 774 776 776 914 914 900 900 776 776 776 478 478 478 478 600 555 555 555 555 555 643 543 543 543 1590 1080 795 435 348 292 222 567 567 567 555 555 555 555 555 555 555 555 616 616 616 616
338 589 675 810 820 283 443 710 727 1360 1140 870 264 295 337 456 238 336 460 489 518 665 594 233 267 295 325 179 221 248 320 337 a92 450 254 343 513 445 606 646 713 310 429 520 547 742 870 960 1070
13,800 25,700 30,300 7,990 9,900 15.200 17.400 18,900 22,000 27.000
534 534 534 4.2 X 4.2 X 4.2 X 4.3 X 4.2 X 4.3 X 4.3 X
697 1110 1310 12.3 15.2 23.4 26.5 29.0 33.6 41.3
m_ _ n_
10'
10s
106 10' 106 106 10'
It was assumed that as a first approximation the dimensionless groups involved in Equation 4 could be expressed as power functions, and the results for several liquid-solid systems in the turbine agitator were correlated by =
(.u)~.~
0.16 ( np)a.6a
for Reynolds numbers greater than 6.7 X lo4,and by
(5)
122
INDUSTRIAL A N D ENGINEERING CHEMISTRY = 2.7
x
10-5 (n?)"
Vol. 34, No. 1
($o.6
for lower values of Re. It was further shown that under isothermal conditions, for any particular liquid-solid system, Equation 4 reduces to: Kd = $(nd2)
(7)
A plot of Kd os. (nd2)for the individual liquid-solid systems reported in the present paper indicated a fair correlation of the experimental data. However, it was shown (2) that when K was plotted against nd, which is equivalent to the peripheral velocity of the impeller, an excellent correlation was obtained for every liquid-solid system. This is further confirmed by the results recorded in the present paper. In Figure 2 dissolution constant K , for the systems rock saltwater and benzoic acid-water in propeller agitators, is plotted against nd, for four different vessels, and the results are correlated by straight lines. The same type of correlation holds for other designs. The data of Hixson and Wilkens (4) for the system benzoic acidwater, as determined in baffled vessels with turbine impellers, are plotted in Figure 3. I n the cases where one, two, four and six baffles were used, the results for three or more experimental points are well correlated by straight lines, with only one major deviation in the case of a run made in the 119-cm. vessel with four baffles. This may have been due to the effect of surface roughness, since the largest tank was not varnished while all other vessels were. The results for tanks with three and five baffles are also shown for comparison purposes, although the lines are not well established in these cases, being based on only two points. The agreement between the experimental points in Figure 2 for the propeller agitators is not so good as that shown in Figure 3 and previous K us. nd plots. This is probably due t o two reasons: the variation from actual geometrical similitude of the different propeller sizes, and the difficulty in obtaining constant speed with this type of equipment. I n general, the results of Hixson and Wilkens deviate less from the average line than do the results of the authors. This can be partly attributed to the fact that Hixson and Wilkens took extensive precautions to maintain a constant temperature (25' C.) in their runs, while no such attempt was made in this research. Elaborate precautions for tempera-
FIGURE 1. DIMENSIONALLY SIMILAR PROPELLER AGITATORS
ture control are not necessary since, as will be shown later, the average temperature a t which any individual run is made establishes the fluid properties; and the temperature variation is automatically compensated for in the more general correlation of the data. From these experimental results it can be stated that, under isothermal conditions, K = +(nd)
VESSELS (4) TABLE 11. MASSTRANSFER DATAIN BAFFLED
(All runs for the system benzoic acid-water a t 25O C.)
No. of
Baffles 1 2
3 4
d 15.2 26.0 45.7 15.2 26.0 45.7 61.0 15.2 26.0 15.2 26.0 45.7 45.7 45.7 45.7
61.0 61.0 61.0 61.0
5
6
15.2 26.0 26.0 45.7 61.0
n 3.33 3.33 3.33 3.33 3.33 3.33 3.33 3.33 3.33 3.33 3.33 1.87 3.33 4.59 5.83 2.08 3.33 4.59 5.83 3.33 3.33 3.33 3.33 3.33
K 0.00340 0.00384 0.00418 n.no320 0.00330 0.00421 0.00467 0.00183 0.00245 0.00133 0.00222 0.00204 0.00344 0.00481 0.00545 0.00303 0.00404 0.00521 0.00596 0.00150 0.00251 0.00212 0.00341 0.00415
nd 50.6 86.6 152 50.6 86.6 152 204 50.6 86.6 50.6 86.6 85.5 152 210 267 127 203 280 356
50.6 85.6 86.6 152 204
( 8)
for any particular liquid-solid system in a series of dimensionally similar agitators. In the correlation of experimental data by means of dimensional analysis, it is customary to express the various dimensionless groups as power functions. If Equation 4 is expressed in this manner, then Equation 7 can be written: Kd = p ( n d 2 ) e
(9)
Equation 8 is incompatible with Equation 9 except for the case where exponent e equals one2; in that case Equation 9 reduces t o K = P(nd)
(10)
But this would mean that the slope of the line on the K US. nd plot should be 1.0. This is approximately true for several cases, In Figure 2 the line for rock salt-water has a slope of 0.90, and the line for benzoic acid-mater has a slope of 1.3. In Figure 3 the line for four baffles has a slope of 0.81, the line for five baffles has a slope of 1.0, and the line for six baffles has 2 In the earlier paper (E)it waa stated that Eauation 7 roduoed t o Eaustion 8. This is true only in the limiting case where B = 1.
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1942
nd 200 300
K 100
nd 500 700
K 30 4050 70 .007 .O06 .005 .004
100
groups K d / D and p/pD. The data were extrapolated to obtain values of D for temperatures greater than 30' C. By this technique a range of p/pD from 222 to 1590 was made possible. A plot was then made of K d / D against Re (Figure 4). The runs made at an average temperature of 25' C. are correlated by a straight line. Parallel to this line, correlating the data at 25' C., a series of lines was drawn through the points for other temperatures. The values of K d / D a t constant Re = lo6 were determined and plotted against p/pD in Figure 5 . Also shown in Figure 5 are points for the systems benzoic acid-water and benzoic acid-benzene at Re = 106. Since at constant Re, Equation 4 (in terms of power functions) becomes
200 300
,003 vessel
.002
26.0
symbol b
.oo I K .005 .004 .003 .002
K
,007 100 FIGURB
200 300 nd 2.
K
US.
500 700
nd IN PROPELLER
T Y P l AGITATORS Abwa, rack palGwater at 23-28' C.; below benzaio acid-water at 22-26' C.
+ FIGURE 3 (Right). K us. nd IN BAFFLED TURBINE AGITATORS FOR BENZOIC ACIDWATERAT 25' C. (TPBLB11)
.006 .005 .004
e D = 8' (-$y
,003
.oo I 30 4050 70 100 nd
(11)
the slope of the line in Figure 5 is the numerical value for y. From the calculated slope of this line, y = 0.44, which is the same as the value Gilliland and Sherwood (1, 6) found
.002
a slope of 0.81. Where the turbine agitator was used with less than four baffles, the lines have a slope appreciably less than 1.0. Since the results for these cases are correlated by the K 08. nd plot, it may be that there is some additional factor to be included in applying dimensional analysis to these designs. Just what this factor is could not be determined in the range of variables considered in the present investigation. Equation 4 indicates that, as a first approximation, if ( K / D ) i(p/pD)T is plotted against @ p / p , a general correlation of data for any one type of apparatus should be obtained if the proper value for y is selected. It was previously assumed that y = 0.5, but this could not be accurately confirmed because of the narrow range of the experimental data. For accurate evaluation of this exponent, a wide range of values for the dimensionless group p/pD is desirable. To obtain this, data in the International Critical Tables on the diffusivity of sodium chloride into water over a temperature range of 5-30" C. were employed in the following manner: A series of runs with the system rock salt-water (included in Table I) was made in the propeller type agitator a t temperatures ranging from 645" C. The reported values for diffusivity were then employed in evaluating the dimensionless
123
200 300
3
2
21 lo0 9 8
7 6 5 4
3 3
4
5
6 7 8 9
2
I ob
Re
3
4
5
a &
Y DETERMIGATION OF K d / D AT Re = lonFOR FIGURE 4. GRAPHICAL ROCKSALT-WATER SYSTEM
INDUSTRIAL AND ENGINEERING CHEMISTRY
124
Vol. 34, No. P
which is in fair agreement with Equation 8, and Equation 12 reduces to K p~~~Jnl.Od1.0 (15)
1.5
210 1 o'+ 9
8 7 6
5 7
200
300 400
600 800 1000
2000
A
QD
OF FIGURE 5. PLOTOF K d / D vs. p / p D FOR EVALUATION EXPONENT y
for the correlation of their data on the rate of vaporization of water and several organic liquids into a turbulent air stream. A similar graphical analysis of the data on mass tranfer in the turbine type agitator ( 2 ) was made, and a value for y of 0.55 was found. This value is based upon a range of ( p / p D ) of only 400-800 for five different liquid-solid systems, all a t approximately the same temperature of 25' C. Because of this narrow range, the value 0.55 should not be considered so accurate as the value of y found for the propeller type apparatus. For the general correlation of data, a more or less average value for y of 0.5 was used. Choice of 0.44 or 0.5 causes practically no difference in the deviation of any group of data from the average line. Experimental results for the propeller agitators are shown in Figure 6 where ( K d / D ) +- (p/pD)Oe5 is plotted against Re. All data are correlated by a single straight line having a slope of 1.0. The equation of this line is: = 3.5 x 10-4
which is in excellent agreement with this relation. Equations 5 and 6 should be considered as approximately averaging the results for several systems, since examination of Figure 4 of a previous paper (a) indicates that the points for any liquidsolid system in a vessel of a single size tend to fall on both sides of the average line, and the slopes of the lines drawn through these points is much lower than the slope of the average line. This same effect is not so apparent in the K us. nd plots for the same systems. Here again there is some indication that an additional variable should be included in the general correlation for the turbine design without baffles; and while its omission causes no serious error over the range of the experiments, a t lower and higher values it may become serious. This unknown variable may also explain the inconsistencies in the agreement of Equations 13 and 14 with Equation 8.
Comparison of Designs For the propeller type agitators, considerably higher speeds compared to those used in the turbine agitators were necessary to keep the solid particles off the bottom of the can. This may be attributed t o the larger area of the turbine impellers and the fact that the direction of rotation in the case of the turbine forced the liquid up, while in the case of the propeller the liquid was forced dox-n. Speeds up to 1100 r. p. m. were
(?Yo
The absence of a critical Reynolds number for this type of design may be due to the nonsymmetry of the equipment compared to the turbine design. Under isothermal conditions, for dilute solutions Equation 5 reduces to K =
(6"nO.62dO.24
(13)
which is apparently inconsistent with the experimentally derived relation, K =d
n4
( 8)
fi~~)~1.4di.a
2
3
4 5 6 7
Re.&
Y
Equation 6 reduces to K =
3 4 5 6 7 8 IO'
(14)
FIGURE 6. GEKERAL CORRELATION OF DATAON MASSTRAMPER IN PROPELLER TYPEAGITATORS
January, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
used with the propellers, particularly in the case of the smaller sizes. Higher rotational speeds caused appreciable splitting of the benzoic acid tablets since the length of time for runs with the system benzoic acid-water was comparatively long (10-15 minutes), and the subsequent opportunity for the rapidly rotating impeller to come in contact with a solid particle was great. The lines correlating mass transfer data in the turbine type agitator (2) are also shown in Figure 6 for comparison. Apparently for the two designs studied, the turbine gives appreciably better results, as far as mass transfer is concerned, when compared to the propeller. However, this should not be interpreted as meaning that turbine agitators are better than propeller agitators since other factors, such as power requirements, cost of equipment, and the effect of a minor change in design, should also be included in the analysis. Indeed, most turbine-type agitation equipment is built with vertical baffles which have the effect of reducing the mass transfer coefficient, K , at any given Reynolds number and a t the same time of sharply increasing the power requirements (4).
Thermal Effects Due to Dissolution Thermal effects of the dissolution process were disregarded in the integration of Equation 1. This is justifiable since the heat of solution has little effect on the film conditions for the systems studied. For example, if one starts with a quantity of water at 25" C. and adds sufficient sodium chloride to saturate this amount of water, maintaining adiabatic conditions throughout the process, available heat of solution and specific heat data indicate that the resulting temperature drop will be approximately 3" C. Since a condition of saturation at the liquid-solid interface is assumed in the mass transfer process, it follows that the lowest interfacial temperature possible, in an experiment involving the rate of solution of sodium chloride in water, will be 22" C. when all materials are initially a t 25" C. Choice of 22" for evaluation of the interfacial saturation solubility in place of 25" will cause a difference of only 0.3 per cent in the calculated dissolution constant for the system sodium chloride-water. Since this is theoretically the lowest temperature possible, and actually some other temperature between 22" and 25" C. is attained b e cause of heat flow from the bulk fluid into the film, the error in the dissolution constant is probably less than the value shown above. For the system benzoic acid-water the solubility of the solid is so small that thermal effects are also small, and there is no large difference between the interfacial temperature and the initial temperature of the materials. Other systems studied in this work could not be investigated in a similar manner because of a lack of thermal data, but it is likely that thermal considerations can be neglected in the evaluation of the dissolution constants for these.
Conclusions 1. For several different agitator designs, it is shown that the dissolution constant for any liquid-solid system under isothermal conditions is a function of the product of speed and size factor. 2. The results for a number of liquid-solid combinations in any single agitator design are included in a single correlation where the variables-effective lilm thickness, viscosity, liquid density, diffusivity, rotational speed, and size factorare included in the plotted terms. 3. Mass transfer results obtained over a range of temperatures are included in the general correlation of data for any one agitator design by taking into account the effects of temperature on the physical properties considered in the correlation.
125
4. Comparison is made between the turbine and propeller as an agitating device, and for the range of sizes studied, the turbine, operating without baffles, gives higher values for the dissolution constant in liquid-solid agitation. 5. Thermal effects due to the dissolution process are shown to have a negligible influence on the value of the dissolution constant.
Acknowledgment The authors are indebted to the Mixing Equipment Company of Rochester, N. Y . ,who supplied the propellers used in this work.
Nomenclature A A, A6
C C,
d
D e
K
= surface area, sq. cm. = average surface area, sq. cm. = initial surface area, sq. cm. 5
=
= = = =
n Re
--
T
=
W
=
=i
WO X, = 8, y = A A0
p
e
f
= = = = = =
concentration, grams solute/cc. solvent concentration at saturation, grams solute/cc. solvent vessel diameter, cm. diffusivity, sq. cm./sec. constant mass transfer coefficient, grams/(sec.) (sq. cm.)(unit concn. change in grams/cc.) stirrers eed, revolutions/sec. Reynolls number = (nd*p)/p for agitation systems, no dimensions temperature, C. weight of undissolved solid at time 0, grams initial wei ht of solid, grams effective thickness for mass transfer, om. constants concentration driving force = (C, - C), grms/cc. initial concentration driving force, grams/cc. density of solvent, grams/cc. time, sec. viscosity, grams/(sec.) (om.) mathematical symbol representing "function of"
&
Literature Cited (1) Gilliland, E. R., and Sherwood, T. K., IND.ENO.CREW.. 26.
616 (1934). (2) Hixson, A. W., and Baum, S. J., Ibid., 33, 478 (1941). (3) Hixson, A. W.,and Crowell, J. H., Ibid., 23, 923, 1002, I160 (1931). (4) Hixson, A. W., and Wilkens, G. A., Ibid., 25, I196 (1933). (6) Sherwood, T. K., "Absorption and Extraction", Chap. 2, New York,McGraw-Hill Book Co., 1937. I-
--I
